A process tank has two input streams-Stream 1 at mass
flow rate w1 and Stream 2 at mass flow rate w2. The tank's effluent
stream, at flow rate w, discharges through a fixed valve
to atmospheric pressure. Pressure drop across the valve is
proportional to the flow rate squared. The cross-sectional
area of the tank, A, is 5 m2, and the mass density of all
streams is 940 kg/m3.
(a) Draw a schematic diagram of the process and write an
appropriate dynamic model for the tank level. What is the
corresponding steady-state model?
(b) At initial steady-state conditions, with w1 = 2.0 kg/sand
w2 = 1.2 kg/s, the tank level is 2.25 m. What is the value of the
valve constant (give units)?
(c) A process control engineer decides to use a feed
forward controller to hold the level approximately constant
at the set-point value (hsp = 2.25 m) by measuring w1 and manipulating
w2. What is the mathematical relation that will be
used in the controller? If the w1 measurement is not very accurate
and always supplies a value that is 1.1 times the actual
flow rate, what can you conclude about the resulting level
control? (Hint: Consider the process initially at the desired
steady-state level and with the feedforward controller turned
on. Because the controller output is slightly in error, w2 of. 1.2,
so the process will come to a new steady state. What is it?)
What conclusions can you draw concerning the need for accuracy
in a steady-state model? for the accuracy of the measurement
device? for the accuracy of the control valve? Consider
all of these with respect to their use in a feedforward control
system.